Difference between revisions of "Trapezoid"
(Converted to new hexboard diagrams, and added missing material on dominated moves in the trapezoid) |
(→Dominated cells: Updated the argument about dominated cells. The new one might still be wrong.) |
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contents="R a3 b1 c1 c3 E *:a2" | contents="R a3 b1 c1 c3 E *:a2" | ||
/> | /> | ||
| − | + | To see why, note that Red can play the following pairing strategy. | |
| + | <hexboard size="3x3" | ||
| + | coords="none" | ||
| + | edges="none" | ||
| + | visible="-a1" | ||
| + | contents="R a3 b1 c1 c3 E a:a2 a:b2 b:c2 b:b3" | ||
| + | /> | ||
| + | If Blue plays in one of the cells marked "a", then Red plays in the other one. Similarly, if Blue plays in one of the cells marked "b", Red plays in the other one. The end result is that all of Red's pieces are connected, and any Blue pieces other than in "*" are dead. Since Blue cannot achieve anything better than to get "*", playing at "*" immediately is at least as good as playing anywhere else in the template. In other words, from Blue's point of view, "*" [[dominated cell|dominates]] all other possible moves in the trapezoid's carrier. | ||
| − | The same holds from Red's point of view as well. If Red is to play anywhere in | + | The same holds from Red's point of view as well. If Red is to play anywhere in the trapezoid's carrier, the only sensible move is at "*", because this [[captured cell|captures]] the rest of the carrier. |
[[category:interior templates]] | [[category:interior templates]] | ||
[[category:basic Strategy]] | [[category:basic Strategy]] | ||
Revision as of 06:21, 7 December 2020
The mouth or trapezoid is an interior template with a wide base. It is one of the most common interior templates after the bridge. The carrier of the template, i.e., the set of cells that must be empty for the template to be valid, is shown in the following diagram.
Common patterns
Gaining Ground
The mouth can be used to steal territory. For example, in the following situation
Red can play as follows:
Ladder Escapes
The mouth also allows some ladder escape constructions.
Dominated cells
If Blue wants to intrude into the trapezoid, the only possible intrusion point is the hex marked "*".
To see why, note that Red can play the following pairing strategy.
If Blue plays in one of the cells marked "a", then Red plays in the other one. Similarly, if Blue plays in one of the cells marked "b", Red plays in the other one. The end result is that all of Red's pieces are connected, and any Blue pieces other than in "*" are dead. Since Blue cannot achieve anything better than to get "*", playing at "*" immediately is at least as good as playing anywhere else in the template. In other words, from Blue's point of view, "*" dominates all other possible moves in the trapezoid's carrier.
The same holds from Red's point of view as well. If Red is to play anywhere in the trapezoid's carrier, the only sensible move is at "*", because this captures the rest of the carrier.
